The air layer of thickness Δx at a distance x from the front of the cabin experiences the force of pressure
where * is the cross-sectional area of the cabin. Since air is at rest relative to the cabin, the equation of motion for the mass of air under consideration has the form
Making Δx tend to zero, we obtain
Since the mean pressure in the cabin *** unchanged and equal to the atmospheric pressure ρ0, the constant p1 can be found from the condition
where l is the length of the cabin. Thus, in the middle of the cabin, the pressure is equal to the atmospheric pressure, while in the front and rear parts of the cabin, the pressure is lower and higher than the atmospheric pressure by
respectively.
